1

DesignCon 2016

Characterizing Geometry-

Dependent Crossover

Frequency for Stripline

Dielectric and Metal Losses

Svetlana C. Sejas-GarcíaChudy NwachukwuIsola

2

Abstract

Digital signaling requires interconnects operating at microwave frequencies to achieve

current data transfer demands in computing platforms. Therefore, the performance

assessment of these interconnects is mandatory in order to visualize their range of

usability and limitations so that a systematic design and implementation of prototypes

and final products can be achieved. In this regard, the limitations of the interconnects are

associated with two types of losses: i) those associated with signal reflections

(mismatch), which are quantified through the return loss, and ii) those associated with

physical losses originating from dissipation of energy, which are quantified by the

insertion loss. Whereas both types of losses are important from a circuit design

perspective, the latter is more important for material developers in the PCB industry. For

this reason, in order to evaluate the suitability of a given material for particular

applications within certain frequency bands, several figures of merit have been defined.

The most commonly used terms in the PCB industry are the permittivity or dielectric

constant (Dk) and dissipation factor (DF) of dielectrics, and the conductivity and surface

roughness for metals. Nevertheless, until now there are no unique figures of merit that

account for both dielectric and metal losses in a simultaneous way. A parameter like this

can be very useful when identifying what PCB interconnect material(s) would negatively

affect overall performance in a more accentuated way .

In this paper, the crossover frequency (CF) for the metal and dielectric attenuation curves

is proposed as a figure-of-merit to indicate the frontier dividing the frequency band where

the dielectric losses overpass metallic losses and vice versa. Particularly, striplines are

analyzed here in order to avoid introducing parameters such as the filling-factor

requirement for studying multi-dielectric configurations (e.g., microstrip lines). The

importance of the CF parameter relies on the its ability to determine material

performance by comparing the corresponding losses with those introduced by either the

metal or dielectric counterpart. Thus, when considering a fixed PCB substrate thickness,

similar widths for striplines would be required to obtain target impedance in different

materials. In this case, higher CF would indicate superior dielectric performance.

Similarly, when scaling down the substrate thickness and keeping the material properties

constant (and maintaining the corresponding losses), the stripline dimensions should be

reduced accordingly, thereby increasing CF and indicating that the metal losses would be

dominant in a wider band. This paper will explore the variation of CF with geometry,

materials, and structure (e.g., metal roughness) for striplines. This would point out the

usefulness of this parameter to provide the designer with information about the main loss

factor attributed to a given PCB interconnect. With this information, the designer can

make an informed decision on selecting a cost-effective solution for a certain application,

and in addition the material developer would get feedback to meet the requirements for

the materials forming the interconnects.

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Authors Biography

Svetlana C. Sejas-García is an engineer in Isola's R&D team. She was born in Puebla,

Mexico, where she received the B.S. degree in Electronics from the Benemérita

Universidad Autónoma de Puebla, in 2005 and the Ph.D. degree in Electronics from

INAOE, in 2014. She performs research on the effects occurring in chip-to-chip

communication channels and passive components. In 2008, she was an Intern with Intel

Laboratories, Mexico, working on the development of models for high-speed

interconnects.

Chudy Nwachukwu manages the Signal Integrity Laboratory and SaaS Application

Development for Isola USA Corp located in Chandler, Arizona. His previous work

experiences with Force10 Networks and Gold Circuit Electronics included but were not

limited to; PCB interconnect design, project management, research and development, and

technical sales / marketing. Chudy received his MBA degree from Arizona State

University; and M.S.E.E. degree from Saint Cloud State University. He graduated with a

Bachelor's degree in Mathematics and Computer Science from Southwest Minnesota

State University in Minnesota.

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1 Introduction

The selection of appropriate PCB materials is the first step towards the development of a

successful circuit design. In the past, this selection was based primarily on mechanical and

thermal considerations because there were no significant problems encountered from the

electrical routing of the signal and power paths at relatively low data rates. As data rates have

increased to reach transfer levels in the range of gigabits per second, accounting for fundamental

transmission line concepts in circuit design has become mandatory. In this regard, the

corresponding delay and losses introduced by the non-ideal properties of the media where the

signals propagate affect the integrity of the digital information sent from one point to other within

a circuit. Thus, it is important for the circuit designer to minimize these effects by selecting

appropriate materials for implementing interconnect channels operating at a given bandwidth.

On the other hand, it is important to bear in mind that the PCB industry is largely driven by cost-

benefit considerations. Although advanced dielectric substrates and metal foils are available to

implement high-performance PCBs, these top-of-the-line solutions are not always the most

appropriate for all applications. For instance, one would not use ultralow-loss dielectrics to

implement circuits operating at slow data-rates. The circuitry would perform to specification with

the use of typical FR4 laminated with rougher metal foils.

In order to aid the selection of an appropriate combination of materials, the performance

characterization should begin with the determination (or at least an estimation) of the separate

contribution of the conductor and dielectric losses to the total attenuation occurring on a PCB

interconnect. Recently, much research has been performed in this direction based on the fact that

dielectric and conductor loss data present different functional forms when plotted versus

frequency [1]. The corresponding models may include several terms accounting for the different

effects that occur when the signal is interacting with the media where the channel is implemented

[2]. Even more elaborate models may be implemented by processing experimental data, thus

providing a good idea of the contribution of each type of material loss to the attenuation [3]. On

the other hand, simpler models are handy when limited bandwidths are being considered or when

higher order effects such as the conductor-dielectric surface roughness introduces little change in

desired properties. In this particular case, the dielectric losses can be considered proportional to

frequency and conductor losses proportional to the square root of the frequency [4]. However,

this approximation is only applicable to a very limited number of cases in PCB technology that is

constantly evolving and dealing with continuously increasing data rates.

In spite of the afore-mentioned efforts geared at providing a unified and generalized

methodologies to separating the dielectric and conductor losses, much work remains to be

accomplished on this subject. In fact, a recent DesignCon paper [5] clearly stated the difficulties

entailed in separating these losses due to the fact that additional resistance related to the surface

roughness introduces frequency dependent effects that may present similar trends to those

observed on the dielectric. In fact, due to the random nature of the surface roughness, most

models are either based on empirical equations [6] or based on statistical data [7]. For current

technologies, a proper use of these models allows for an accurate representation of the conductor

attenuation and may eventually be used to determine the dielectric losses when the total

attenuation is known. Furthermore, once the conductor and dielectric losses are known, it is

possible to determine the frequency at which the dielectric attenuation surpasses the conductor

attenuation. The use and importance of this frequency point as a figure-of-merit is analyzed in

this paper.

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a b

Figure 1. Conceptual sketch illustrating the current distribution (in yellow) within the cross section of a stripline with equidistant ground planes under DC conditions (a), and once the skin depth is smaller than the thickness of the trace (b).

t

W H1

H2

t

W H1

H2

To develop the concept proposed in the previous paragraph, this paper reports in-depth analysis

based on physical experiments and full-wave simulations of striplines. We focus on stripline

structures in order to avoid the variations in manufacturing and additional effects occurring in

microstrip lines (e.g., frequency-dependent filling factor).

Losses in a transmission line

Signal power losses represent one of the main concerns for signal integrity engineers, especially

as data rates increase and the cross sectional area of interconnects shrink. Therefore, when

designing a PCB, mismatches in electrical transitions, parasitic effects, and unwanted coupling

effects are avoided as much as possible. However, the intrinsic material losses cannot be avoided

and should be taken into consideration from the early stages of the design process. In this regard,

high-speed signaling interconnects are treated as transmission lines affected by losses that can be

separated into three main categories: conductor losses, dielectric losses, and radiation. For

striplines and at the frequencies of interest in this paper, losses due to radiation can be considered

much smaller in comparison, so we can associate the experimentally obtained attenuation with

just the conductor and dielectric losses.

Conductor Losses

These losses are associated with the finite conductivity of the traces used to form the

interconnects. Thus, the corresponding resistance dissipates power due to the joule effect, a

known issue at high frequencies. Moreover, as the industry of electronics is evolving towards

higher density interconnects and packages, the cross section of interconnects are being

considerably scaled down. This comes with a corresponding increase of the resistance associated

with the metal traces, which can be obtained (assuming DC conditions) as:

𝑅𝐷𝐶 = 𝜌 𝐿

𝐴=

𝜌 𝐿

𝑤𝑡 (1)

where ρ is the resistivity of the conductor material (usually copper), A = wt, and L, w and t are the

trace’s length, width, and thickness, respectively. Notice that in this equation (1), the resistance

associated with the return path is neglected since the corresponding width is much larger than the

width of the metal trace. Fig. 1a illustrates that the current can be assumed to be homogeneously

distributed in the cross section of a stripline.

For current PCBs and packages, RDC is very low due to the relatively large cross section of the

interconnects. However, as frequency increases, the effective area from which the current is

flowing is reduced due to the skin effect, which increases the resistance and consequently the

signal attenuation. This reduction only occurs when the skin depth (δ) of the conductor used to

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form the interconnect becomes comparable to its dimensions. In this case, a way to incorporate

the skin effect into the model for the resistance requires a mathematical representation of the skin

depth; this is:

where ρ is the resistivity of the material conductor, f the frequency and μ is the permeability of

free space.

It can be demonstrated that a good first-order approximation for determining the frequency-

dependent cross-sectional area A in (1) is achieved by utilizing δ in the following fashion. For a

typical PCB stripline w>t; A would be first modified by a change in thickness once δ ≤ t. In this

case, the resistance of the signal trace can be represented by means of the following equation:

where t in (1) is substituted by 2δ due to the skin effect at higher frequencies where current is

confined to the upper and lower edges of the metal trace, as illustrated in Fig. 1b. As expected,

RAC_trace is proportional to the square root of frequency due to its dependence on δ. Bear in mind,

that in an actual interconnect the skin effect impacts the current distribution in all directions and

within all the metals forming the interconnect. Furthermore, by assuming the use of smooth

conductors and considering that the frequency is so high that the skin effect is simultaneously

modifying the current distribution of the signal trace and the ground plane, it is reasonable to

assume the following for the total AC resistance of the line:

or

where Rs can be considered approximately constant at microwave frequencies. Thus, the increase

of the resistance with frequency predicted by (3) yields that the conductor loss for lines with

smooth surfaces are also proportional of the square root of the frequency [8]. Fig. 2 shows a curve

illustrating the onset frequency of the skin effect (i.e. the minimum frequency at which the

resistance becomes frequency dependent) for different standard foils used in PCB manufacturing.

Since striplines are considered in this case, the onset frequency is determined when δ = t/2.

Notice that for all foils the onset frequency is below 1 GHz. For any high-frequency signals near

the surface of the metal traces, the profile of the surface becomes an important factor to be

considered when determining the conductor losses.

As it is widely known, the presence of roughness in the conductor material is necessary to

improve adhesion to dielectrics in order to avoid delamination. Currently, there are different types

of copper foils which present values of rms roughness (hrms) from less than 5 microns to 10

microns; some of the most representative are shown in Fig. 3 [9]. Accurately modeling the

surface conductor roughness is fundamental to accurately predicting the interconnect performance

since the contribution of the surface roughness effect at high frequencies can reach 10%–50%

[8,10].

𝛿 = √ 𝜌

𝜋𝜇𝑓 (2)

𝑅𝐴𝐶_𝑡𝑟𝑎𝑐𝑒 =𝜌 𝐿

2𝛿𝑤 (2)

𝑅𝐴𝐶 ∝ √𝑓

𝑅𝐴𝐶 = 𝑅𝑠√𝑓 (3)

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Figure 2. Skin depth versus frequency curve for copper illustrating the onset frequency for the skin effect for standard foils used in PCB technology (striplines are considered).

Figure 3. Illustration of different copper profiles currently used in PCB technology.

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30

35

40

1/4 Oz (8.89 m)

1/2 Oz (17.78 m)

1 Oz (35.56 m)

Skin

de

pth

(

m)

freq (MHz)

2 Oz (71.12 m)

Ve

ry L

ow

Pro

file

Co

ppe

r

Much work has been reported over the last three decades about the losses introduced by the

imperfect surface of metal traces. Three of the most popular models among engineers for

considering this effect are:

1. Hammerstad & Jensen’s (HJ) model [5, 6].

2. HJ Modified model [5].

3. Huray’s snowball model [5, 7].

These three models assume that the AC resistance of the line is further increased by an additional

factor KH, which implies that (3) has to be modified to 𝑅𝐴𝐶 = 𝐾𝐻 𝑅𝑠√𝑓. This in turn implies that

the following expression can be written for the attenuation associated with the conductor losses:

𝛼𝑐 = 𝐾𝐻𝐾𝑐 √𝑓 (3)

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where Kc is assumed to be approximately constant and KH is a frequency dependent factor. Thus,

the difference between the three models mentioned above relies in the way KH is represented as a

function of frequency. Notice that for a trace with smooth surfaces, KH = 1. At frequencies at

which the skin depth is much larger than hrms also KH = 1 since the impact of the surface

roughness is not significant. Nevertheless, KH rises with frequency, thereby increasing RAC when

the current flows in the cross-sectional area substantially modified by the surface roughness.

For the case of the HJ model, an empirical relationship between hrms and KH can be found; this is:

When Hammerstad and Jensen proposed (4), they noticed that for frequencies so high that δ ≪ hrms, the interconnect’s resistance increases up to twice the resistance of the same interconnect but

with smooth surfaces. Thus, beyond a certain frequency, KH reaches a saturation value of 2 (i.e. 1

≪ KH ≪ 2). Years later, this was observed as an underestimation of the impact of surface

roughness at high frequencies for conductors with extremely rough surface profiles [5, 7]. For this

reason, a corrected equation was proposed to improve the HJ model, which is given by

This second model is known as the HJ modified model, where the correction roughness factor

(RF) may take values higher than 1; obviously considering RF = 2 yields the classical HJ

equation (4) [5, 11]. The disadvantage of (5) is the lack of a generalized method by which to

obtain RF. In order to overcome this inconvenience, the Huray method was proposed [7, 12],

which uses a representation of the surface roughness through small spheres in flat hexagonal area

cells. These cells are distributed throughout the surface of the metal trace, thus allowing for the

following equation to be obtained:

where Amatte is the surface area, Aflat is the surface area of the hexagonal cells, Ni is the

number of spheres per cell, and ai is the sphere radius. Since the accuracy of this model

depends on the number and radius of the spheres, it is more computationally efficient when all the

feature dimensions of the surface profile are known [5, 7]. It is important to mention that even

though the accuracy of (6) is high when appropriately defining the corresponding parameters, (4)

and (5) present the advantage of being more easily implemented and provide acceptable results at

frequencies of gigahertz (< 20 GHz) for current technologies.

𝐾𝐻 = 1 + 2

𝜋atan (1.4 (

ℎ𝑟𝑚𝑠

𝛿)

2

) (4)

𝐾𝐻 = 1 + 2

𝜋atan (1.4 (

ℎ𝑟𝑚𝑠

𝛿)

2

) (𝑅𝐹 − 1) (5)

𝐾𝐻𝑢𝑟𝑎𝑦 = 𝐴𝑚𝑎𝑡𝑡𝑒

𝐴𝑓𝑙𝑎𝑡+

3

2∑

𝑁𝑖 4𝜋𝑎𝑖2 𝐴𝑓𝑙𝑎𝑡⁄

1 + 𝛿 𝑎𝑖⁄ + 𝛿2 𝑎𝑖2⁄

𝑗

𝑖−1 (6)

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Figure 4. Illustration of the polarization phenomena in a dielectric.

Figure 5. Graphical interpretation of the loss tangent or dissipation factor with two-dimensional vectors.

Unpolarized

+ + + + + + + + + + + + + + + + + + + + + + + + + + + +

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Polarized by external electric field

θ

ε'

-jε”

Dielectric Losses

Dielectric losses are associated with the dissipation of energy in the dielectric substrate and can

be grouped into two main categories: losses due to polarization currents and losses due to

conduction currents. Whereas the latter is negligible on PCB dielectrics, losses due to the

polarization of the dielectric are significant at microwave frequencies. In order to explain the

polarization phenomena, dielectric materials can be thought as a cluster of closely spaced electric

dipoles. These dipoles react to signals by vibrating when tending to align with the associated

time-varying electric field (see Fig. 4). During this process, energy is both stored and absorbed by

the material thereby contributing to signal delay and attenuation. In fact, as frequency increases,

the losses increase because more energy per unit time is absorbed.

The parameter that allows for the quantification of the delay and attenuation occurring in a

dielectric media is the complex permittivity [1]:

휀 = 휀 ′ − 𝑗휀 ′′ (6)

From a signal integrity engineer’s point of view, the real part 휀′ quantifies the speed of

propagation (i.e., the higher 휀′ the slower the propagating signal), meanwhile the imaginary part

−휀′′ relates to the losses occurring in the material. For characterization purposes, the dielectric

losses can be described by the so called loss tangent (tanθ) or dissipation factor (DF), which is the

ratio of the imaginary to the real part of the complex permittivity. Fig. 5 shows a graphical

interpretation of this parameter that is expressed by:

𝐷𝐹 = tan𝜃 = 휀 ′′

휀 ′ (7)

In PCB dielectrics, DF is a parameter that dramatically depends on the resin content, resin type,

frequency, and effects associated with the fiber glass weave.

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Considering DF, an expression can be written for the attenuation due to the dielectric losses; this

is [13]:

𝛼𝑑 =𝐷𝐹 × 𝛽

2 (8)

where β is the phase delay given by the imaginary part of the propagation constant (γ). Thus,

assuming a weak variation of DF and ϵr with frequency (which implies that β is a linear function

of frequency), which is a reasonable assumption for the purposes of this research; the following

alternative expression can be written for αd:

𝛼𝑑 = 𝐾𝑑 𝑓 (9)

In (8), Kd is a proportionality constant. This expression (9) together with (3) will quantify the

crossover frequency as explained in the following sections.

Crossover frequency: definition and determination

At microwave frequencies, it is possible to express the total attenuation occurring in a PCB

transmission line by means of

where (3) and (9) are used to represent the conductor and dielectric losses respectively. When

selecting the most appropriate combination of PCB substrate and copper foil for a particular

application, it is important to determine which one of the two terms on the right hand side of (10)

is more significant within the frequency range of interest. Thus, when the term related to the

dielectric losses is significant and even higher than that related to the conductor losses, the

designer may consider to ask the PCB supplier for a substrate material with reduced losses. It is

tempting to assume that when the opposite occurs, thicker copper foils with diminished surface

roughness would improve the interconnect performance. Well, this is not always the case;

because thickening the copper foil would only reduce the DC resistance of the lines and losses

would be lowered only at low frequencies. Similarly, reducing the surface roughness of the metal

traces within certain limits may present only a small improvement on the interconnect

characteristics if the dielectric losses are too high. Thus, knowing the frequency at which the

contribution of the conductor and dielectric losses to the total attenuation is the same, makes it

possible to improve the performance of the interconnect by changing the characteristics of either

the dielectric or the metal below or above this frequency. Moreover, the sensitivity of the

crossover frequency to changes in materials and geometry of the interconnect provides

information about the corresponding benefits of these changes. This sensitivity analysis is

discussed in greater detail later in this paper.

The crossover frequency (fθ) is defined as the frequency at which αc = αd [4]. Thus, due to the

shape of the curves related to each one of these attenuation components, the dielectric losses

surpass the conductor losses beyond fθ. This is graphically shown in the plots on Fig. 6. Notice

that for the particular example illustrated in this figure, reducing DF by ~35% increases fθ by one

order of magnitude. Nevertheless, it is necessary to mention that from a material fabrication

process, it is difficult to modify DF while maintaining Dk constant. Therefore, the cross section

of the line has to be modified accordingly to retian the target impedance. In Fig. 6, for instance,

the substrate with lower dielectric loss is thinner and also exhibits a lower permittivity. In this

case, the 50-Ω stripline is narrowed compared to the strip width on the other substrate. This

𝛼 = 𝐾𝐻𝐾𝑐 √𝑓 + 𝐾𝑑 𝑓 (10)

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implies that the conductor losses are also higher, and this contributes to further increasing the

crossover frequency. Although in general terms a reduction of the dielectric losses would increase

fθ, it is necessary to analyze in a systematic and controlled way, the corresponding impact of

changing the material properties and geometry.

In this work, two approaches are applied to obtain the crossover frequency: i) directly from

experimentally obtained attenuation data, and ii) using full-wave simulations.

Determination from experimental data

When determining fθ from experimental data, the first step is obtaining the curves that represent

the separate contribution of the conductor and dielectric losses from the total transmission line

loss. In this case, experimental attenuation versus frequency curves is used to determine the

attenuation components due to the conductor and dielectric losses. For this purpose, the following

formulation is employed. Firstly, (10) is divided by the product of 𝐾𝐻 × √𝑓, which yields:

(a)

(b)

Figure 6. Crossover frequency for 50- striplines lines fabricated on different PCB substrates.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

30

35

Dielectric (nominal values): Dk = 3.8, DF = 0.006, h = 7.3 mil

Conductor: copper, 1 oz, RTF, line width= 6.4 mils

conductor attenuation

dielectic attenuation

f = 1.3 GHz

(

dB

/m)

Frequency (GHz)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

30

35

(

dB

/m)

Frequency (GHz)

Dielectric (nominal values): Dk = 3.3, DF = 0.0034, h = 3.5 mil

Conductor: copper, 1/2 oz, RTF, line width: 4.2 mils

conductor attenuation

dielectic attenuation

f = 10.4 GHz

12

Notice that this step allows for the consideration of (11) as the equation of a straight line, where

y = α/KH√𝑓 and x = √𝑓/KH represent the dependent and independent variables, respectively. It is

important to point out the fact that KH is obtained by applying (5), whereas Kc and Kd are

considered as constant as explained when defining (8) and (9). Therefore, performing a linear

regression of y versus x data, Kd and Kc can be obtained from the slope and intercept with these

ordinates, respectively. Bear in mind that considering the appropriate model for the effect of

surface roughness is fundamental to obtaining accurate and meaningful results. In fact, either

ignoring the impact of surface roughness or misrepresenting it may lead to incorrect conclusions

since the corresponding effect may be considered as part of the αd curve. For this paper, the HJ

𝛼

𝐾𝐻√𝑓= 𝐾𝑐 + 𝐾𝑑

√𝑓

𝐾𝐻

(11)

(a)

(b)

Figure 7. Determination of the conductor and dielectric attenuation curves from experimental data: a)

regression for obtaining the model parameters, and b) model implementation.

0 10000 20000 30000 40000 50000 60000 70000 800000

20

40

60

80

100

120

140

160

180

intercept: Kc = 5010

-6

slope: Kd = 1310

-10

Dielectric (nominal values): Dk = 3.3, DF = 0.0034, h = 5 mils

Conductor: copper 1/2 oz, VLP, line witdh = 5.3 mils

experimental data

linear fit

HKf

( fKy

H

y (

10

-6)

f = 24 GHz

0 2 4 6 8 10 12 14 16 18 20 22 240

10

20

30

40

50

60

Dielectric (nominal values): Dk = 3.3, DF = 0.0034, h = 5 mils

Conductor: copper 1/2 oz, VLP, line witdh = 5.3 mils

experimental data

analytical model

conductor attenuation

dielectric attenuation

fanalytical model

= 7.62 GHz

(

dB

/m)

Frequency (GHz)

13

Modified model in (5) was used, which accurately represents the metal surface roughness and

simplifies the analysis [5]. The linear regression involving equation (11) is shown in Fig. 7a,

where the obtained values are: Kc = 50×10-6 and Kd = 13×10-10. Fig. 7b shows that by using these

values, the total attenuation versus frequency data can be accurately reproduced within the

considered frequency range. Moreover, the conductor [equation (3)] and dielectric [equation (9)]

attenuation curves are also shown in this figure, which allows for the straightforward

determination of the crossover frequency.

Determination from full-wave simulations

Even though obtaining fθ from experimental data is desirable since measurements reflect the

properties of the involved materials, a large number of prototypes would be required to carry out

a systematical study like the one presented in this paper (e.g. multiple dielectric materials with

different properties, copper foils, roughness profiles, etc.). Fortunately, the analysis can be carried

out by carefully performing a series of full-wave simulations as explained shortly.

When the experimental attenuation per-unit-length of a stripline geometry is known, these data

can be used as a target for calibrating a 3D model using a full-wave solver. For instance, on the

prototype described in Fig. 8, the model for the attenuation is shown to be in agreement with the

experimental curve after performing parameterized simulations considering the nominal

specifications corresponding to the materials used to build the prototype. Once the model is

calibrated, new simulations are carried out assuming that changing the dielectric properties does

not affect the metal losses and vice versa. In this case, the conductor attenuation can be obtained

by simulating the calibrated model after defining the dielectric as lossless (see red curve in Fig.

8). Likewise, the dielectric attenuation is obtained through simulations considering that the metals

behave as perfect electric conductors (PECs). Notice that using the resulting curves, the value for

fθ is graphically obtained in Fig. 8, and approximately corresponds to the same parameter

obtained from experimental data in Fig. 7. This procedure can be repeated by changing the

properties of the involved materials to analyze the sensitivity of fθ to these variations. In fact, the

usefulness of this approach is explained below.

Figure 8. Correlation of full-wave simulations with experimental attenuation data for determining

conductor and dielectric attenuation curves.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150

10

20

30

40

ffullwave simulation

= 7.5 GHz

(

dB

/m)

Frequency (GHz)

Dielectric (nominal values): Dk = 3.3, DF = 0.0034, h = 5 mils

Conductor: copper 1/2 oz, VLP, line witdh = 5.3 mils

experimental data

fullwave simulation

conductor attenuation (with DF=0)

dielectric attenuation (with PEC)

14

Experiments

Varying length stripline configurations targeting 50 Ω impedance were implemented in four

different prototype PCBs; two prototypes were fabricated using a mid-performance PCB laminate

(nominal Dk = 3.8, DF = 0.006), and two more were fabricated on a high-performance PCB

laminate used for microwave applications (nominal Dk = 3.3, DF = 0.0034). The difference

between the two boards in each material is the surface roughness of the copper foils used; reverse

treat foil (RTF) with rms roughness hrms = 4 μm was used to laminate the mid-performance

dielectric material, and very low profile (VLP) foil with hrms = 2 μm was used to laminate the

high-performance dielectric. The cross sections corresponding to the lines in each one of these

prototypes are shown in Figures 9 and 10. Also, note the different cross-sectional area for the

striplines in each case; the impact of this difference will be discussed in greater detail shortly.

(a) (b)

Figure 9. Cross section of striplines on standard PCB material (Dk = 3.8, DF = 0.006) using different copper foils: a) RTF (hrms ≈ 4 μm), and b) VLP (hrms ≈ 2 μm).

(a) (b)

Figure 10. Cross section of striplines on high-performance PCB material (Dk = 3.3, DF = 0.003) using

different copper foils: a) RTF (hrms ≈ 4 μm), and b) VLP (hrms ≈ 2 μm).

Figure 11. Photograph of one of the PCB prototypes detailing the location of the striplines.

15

In order to perform S-parameter measurements, coaxial K-type microwave connectors were

attached to the boards to terminate the striplines and interface directly with the measurement equipment. Fig. 11 shows a photograph of one of the prototypes. Before performing the

measurements, a vector network analyzer (VNA) setup was calibrated using a two-port electronic

auto-calibrator, which establishes a reference impedance of 50 Ω and shifts the measurement

plane up to the cable connectors to be matched with the prototypes. The setup is shown in Fig. 12.

S-parameter measurements from striplines with varying lengths for all the prototypes were

obtained. These measurements, include the effect of the connectors required to access the PCB

traces. Therefore, a line-line algorithm was employed to obtain the per-unit-length propagation

constant (γ = α + jβ) using the experimental S-parameters of two lines varying only in length [14].

This procedure effectively removes the parasitic effect of the connectors. Afterwards, α = Re(γ) is

obtained for each prototype so that fθ can be experimentally determined as explained before. The

corresponding results are shown in Table I. Notice that due to the difficulty of modifying only

one variable (e.g., surface roughness, stripline cross section, dielectric properties, etc.), the direct

use of measured data does not allow for performing a systematic analysis of the corresponding

effect on fθ. Instead, the experimental data was used to calibrate a 3D model, and then full-wave

simulations were subsequently performed for this purpose.

Figure 12. Setup configured to perform two-port S-parameter measurements.

Material type Copper foil/profile Stripline cross section fθ

Standard 1 oz/RTF 5,276 μm

2 1.3 GHz

1 oz/VLP 4,854 μm2 3.6 GHz

High performance 0.5 oz/RTF 2,068 μm

2 10.5 GHz

0.5 oz/VLP 2,694 μm2 7.6 GHz

Table I: Experimentally determined crossover frequency for the different fabricated prototypes . fθ is affected in these prototypes not only by the changes in the dielectric properties and copper laminate but also on the stripline cross section and variations on dielectric properties (for instance, when fiber weave pattern changes).

16

Impact of changing geometry and material properties on fθ

The experimental data described in the previous section was used to calibrate a 3D model. In

addition, we are assuming that changing the geometry and material properties one at a time

allows for the identification of the corresponding impact on the dielectric and conductor losses,

which in turn can be used to obtain the crossover frequency and study its variation with these

parameters. The following subsections show the results of this analysis.

Stripline width

In this case, the copper foil properties are maintained constant throughout the simulations

performed while considering different stripline widths for achieving characteristic impedances of

25 Ω, 50 Ω, and 75 Ω respectively. Fig. 13 shows the corresponding curves. As expected, higher

characteristic impedance narrows the line and consequently increases the conductor losses.

Therefore, when considering a high performance laminate with low dielectric losses, high values

for the point of intersection for αc and αd are expected. Notice in Fig. 13, for the narrowest line

there is no intersection between the separate attenuation curves. This point out the inconvenience

of using 75-Ω impedance lines at these frequencies for these particular material conditions. An

extreme case is also included in Fig. 13, where αd for a second dielectric represents the loss of a

regular FR-4 laminate (DF = 0.01). Observe that for the three considered impedance cases, fθ is

below 1.5 GHz, indicating that the dielectric losses are much higher than those associated with

the conductor beyond this frequency. This strongly suggests the need of considering a better

laminate within the required frequency range of operation.

Copper foil (trace thickness)

Now, the simulations are performed assuming constant characteristic impedance and different

copper foils for two dielectric materials exhibiting different loss characteristics. Fig. 14 clearly

illustrates the noticeable change in fθ when considering a high performance laminate. As the

copper foil is made thicker, there is more surface area for the current to flow through the cross

Figure 13. Determination of the crossover frequency for lines configured for different impedance assuming

the same PCB conditions.

17

section of the stripline even when the skin effect is accentuated. This approximately reduces 30%

the conductor losses when changing the copper foil from ¼ oz to 2 oz. Nevertheless, this is only

an effective solution when combining the extra copper with a high-performance laminate. As can

be seen in Fig. 14, fθ is significantly reduced (from 11 GHz to about 5 GHz) from the ¼ oz to the

2 oz foil for the low loss laminate. In contrast, a very small change in the crossover frequency is

obtained for the lossier laminate material.

Copper profile (metal surface roughness)

Fig. 15 shows the simulation results when the surface roughnesses of the striplines are modified.

Changes in this parameter also are more relevant from a practical point of view within the

analyzed frequency range when considering a low loss dielectric material. An interesting result

observed through comparing simulations is that for hrms larger than 3 μm, no significant changes

Figure 14. Determination of the crossover frequency for lines presenting different copper foil assuming the same PCB conditions.

Figure 15. Determination of the crossover frequency for lines with different surface roughness and assuming the same PCB conditions.

18

of the conductor losses are observed. In addition, notice that a significant reduction of fθ is

noticeable for values of hrms < 2 μm, which points out the necessity of reducing this parameter

below this value in order to improve the performance of interconnects for high-speed

applications. The theoretical limit in this case is established by hrms = 0 (i.e. a smooth conductor);

for this particular example considering a low loss dielectric laminate, fθ = 2 GHz, where fθ ≈ 7.6

GHz for hrms = 2 μm. Thus, there still remains significant headroom for reducing the metal losses

through smoothing the metal-to-dielectric interfaces. Fig. 16 verifies this fact through the

inspection of the fθ versus hrms curve. Notice the significant change of the crossover frequency for

VLP and RTF foils when using a low-loss dielectric laminate.

Dielectric loss

A final and complementary comparison is shown in Fig. 17, where different dielectric losses are

considered. As the reader will infer from the previous comparisons, better dielectrics (i.e. with

Figure 16. Crossover frequency versus hrms showing the corresponding limits in current PCB technology.

Figure 17. Determination of the crossover frequency for lines with different dielectric losses.

0 1 2 3 4 5 6 7 8 9 102

3

4

5

6

7

8

9

Dielectric (nominal values):

Dk = 3.3, DF = 0.0034, h = 5 mils

Conductor: copper 1/2 oz,

line witdh = 5.3 mils

Line impedance 50

f _hrms 2m

= 7.6 GHz

f _hrms 1m

= 5.7 GHz

crossover frequency

f _smooth

= 2.6 GHz

f_hrms 3m

= 7.9 GHz

f (G

Hz)

hrms

(m)

19

lower loss) push fθ out to higher frequencies and this parameter is very sensitive to improvements

on the conductor properties. In contrast, lossy laminate materials will exhibit crossover frequency

values at a much lower megahertz range, which points to poor performance at multi-gigahertz

frequencies. Moreover, in the latter case, no substantial improvement in the performance of

interconnects is expected when improving the characteristics of the metal foils.

Conclusions

PCB characterization experiments and simulations were carried out to show the usefulness of the

crossover frequency for assessing the performance of striplines when considering changes in

geometry and material properties. In lieu of conducting this systematic analysis entirely through

prototype measurements which would require of a great number of samples with strictly

controlled process parameters, it was shown that full-wave simulations are a viable

characterization option provided that the 3D model is implemented through several model-

experiment correlations.

Results highlight that low values of fθ indicate poor dielectric performance and barely noticeable

improvement of the interconnect characteristics when modifying the properties of the copper foil.

In contrast, the attenuation due to the dielectric loss in high-performance laminates will not only

surpass the conductor attenuation at frequencies of gigahertz, but also allows for a substantial

improvement of the interconnection transmission characteristics when smoother copper foil

profiles are used. This conjecture can be systematically identified through the determination of

the crossover frequency. In fact, the results shown also point to the benefits of either reducing

more the surface roughness of high-speed interconnects or fabricating using alternative printed

interconnect processes in combination with advanced low loss laminates.

20

References

1. Howard Johnson and Martin Graham, “High-Speed Signal Propagation Advanced Black

Magic”, Prentice Hall 2002.

2. Koledintseva, M.Y.; Koul, A.; Hinaga, S.; Drewniak, J.L., “Differential and extrapolation

techniques for extracting dielectric loss of printed circuit board laminates”, IEEE MTT-S ,

p 1- 4, June 2011.

3. Koul, A.; Koledintseva, M.Y.; Hinaga, S.; Drewniak, J.L., "Differential Extrapolation

Method for Separating Dielectric and Rough Conductor Losses in Printed Circuit Boards",

IEEE Trans. on Electromagnetic Compatibility, vol.54, No.2, pp.421-433, April 2012.

4. Torres-Torres, R.; Vega-Gonzalez, V.H., "An approach for quantifying the conductor and

dielectric losses in PCB transmission lines", IEEE EPEPS ‘09, pp.235-238, Oct. 2009.

5. Bogatin, E.; DeGroot D.; Huray P.G.; Shlepnev Y., “Which one is better? Comparing

Options to Deescribe Frequency Dependent Losses”, Proceedings of DesignCon 2013.

6. A. F. Horn, J. W. Reynolds, P. A. LaFrance, J. C. Rautio, ” Effect of conductor profile on

the insertion loss, phase constant, and dispersion in thin high frequency transmission lines”,

Proceedings of DesignCon 2010.

7. Stephen H. Hall and Howard L. Heck, “Advanced Signal Integrity for High-Speed Digital

Designers”, Wiley 2009.

8. Stephen H. Hall, Garret W. Hall and James A. McCall, “High-Speed Digital System

Design- A Handbook of Interconnect Theory and Design Practices Designers”, Wiley 2000

9. Alun Morgan, “Low Loss/ High Speed PCB Materials”, Sep. 2012.

http://www.lboro.ac.uk/microsites/research/iemrc/documents/EventsDocuments/2012confe

rence/presentations/A Morgan Low Loss High speed laminates-What is really needed.pdf

10. J. Conrod, “Circuit Material and High-Frequency Losses of PCBs”, I-Connect 007, The

PCB Magazine, pp. 24-29, Feb. 2012.

11. Shlepnev, Y.; Nwachukwu, C., “Roughness Characterization for Interconnect Analysis”,

IEEE International Symposium on Electromagnetic Compatibility, pp. 518-523, Aug. 2011.

12. Paul G. Huray, “The Foundation of Signal Integrity”, Wiley, 2010.

13. M. Cauwe and J. De Baets. “Broadband material parameter characterization for practical

high-speed interconnects on printed circuit board,” IEEE Tran. Adv. Pack., vol. 31, no. 3,

pp. 649–656, Aug. 2008.

14. J.A. Reynoso-Hernández, “Unified method for determining the complex propagation

constant of reflecting and nonreflecting transmission lines,” IEEE Microwave Wireless

Comp. Lett., Vol. 13, pp. 351–353, Aug. 2003.